Well, how exactly do you expect an amplifier with +/-15V supply to produce +/-690V on the output? Try putting 10mV on the input instead. Also if you used a scope instead of a lousy multimeter feature, you would see the output clipping hard to the power rails minus a bit.

You need to delete C4 and C3, and ground the bottom pin of R2. You might also want to decrease R1 to about 1K, or decrease C2 to about 220nF, because that will give you better response to changes in the DC offset level, but you trade it for gain roll-off at frequencies below 10Hz.

Yes it should, but really depends on what kind of mic you have in mind. If you are going to use the lm833 or any other high speed opamp, you should add a 22pF capacitor between output and negative input of the opamp.